Question

Mr. Sandeep was placing an order with his carpenter to make wooden boxes to pack his cotton toys which were to be delivered to his friend. Sandeep wanted 2 types of boxes. The larger one with a dimension of 25cm x 20cm x 5cm and the smaller box with a dimension of 15cm x 12cm x 5cm. Sandeep also told the carpenter that 5% of total surface area is required as extra to cover the overlaps. If the cost of the wood is Rs.4/- cmz, the cost of wood required for supplying 250 boxes of each type would be Rs. ______.[Note:-D0 NOT include spaces in your answer)

Answer 1

Correct Answer: 2184000

To determine the cost of wood required for 250 boxes of each type, we need to calculate the total surface area of both types of boxes, including the extra 5% for overlaps.
1. Surface Area Calculation:
- Larger Box:
    Dimensions: 25 cm x 20 cm x 5 cm
    Surface Area = 2(lw + lh + wh) 
    \[ = 2(25 \times 20 + 25 \times 5 + 20 \times 5) \]
    \[ = 2(500 + 125 + 100) \]
    \[ = 2 \times 725 \]
    \[ = 1450 \text{ cm}^2 \]
    Including 5% extra:
    \[ = 1450 \times 1.05 = 1522.5 \text{ cm}^2 \]
- Smaller Box:
    Dimensions: 15 cm x 12 cm x 5 cm
    Surface Area = 2(lw + lh + wh) 
    \[ = 2(15 \times 12 + 15 \times 5 + 12 \times 5) \]
    \[ = 2(180 + 75 + 60) \]
    \[ = 2 \times 315 \]
    \[ = 630 \text{ cm}^2 \]
    Including 5% extra:
    \[ = 630 \times 1.05 = 661.5 \text{ cm}^2 \]
2. Total Surface Area for 250 Boxes of Each Type:
- Total for larger boxes:
    \[ = 250 \times 1522.5 = 380625 \text{ cm}^2 \]
  - Total for smaller boxes:
    \[ = 250 \times 661.5 = 165375 \text{ cm}^2 \]
  - Total Surface Area:
    \[ = 380625 + 165375 = 546000 \text{ cm}^2 \]
3. Cost Calculation:
 Cost of wood = Total Surface Area \(\times\) Cost per cm\(^2\)
  \[ = 546000 \times 4 = 2184000 \text{ Rs} \]
Thus, the cost of the wood required for supplying 250 boxes of each type is Rs. 2184000.

Answer 2

We can reach the same cost by adding the 5% extra once at the very end, on the combined area of all 500 boxes, instead of adding it to each box type separately.

1. Step 1: Surface area of the larger box is \( 2(25 \times 20 + 25 \times 5 + 20 \times 5) = 2(500 + 125 + 100) = 1450 \) sq cm, and the smaller box is \( 2(15 \times 12 + 15 \times 5 + 12 \times 5) = 2(180 + 75 + 60) = 630 \) sq cm.
2. Step 2: For 250 boxes of each type, the plain area (before the overlap allowance) is \( 250 \times 1450 + 250 \times 630 = 362500 + 157500 = 520000 \) sq cm.
3. Step 3: Adding the 5% overlap allowance on this combined figure gives \( 520000 \times 1.05 = 546000 \) sq cm.
4. Step 4: At Rs. 4 per sq cm, the cost is \( 546000 \times 4 = 2184000 \).

Adding the 5% at the end on the combined area gives the same 546000 sq cm as adding it box by box, confirming the cost.

Therefore, the correct answer is Rs. 2184000.